Library / Heat transfer and thermal systems / HTS-42
Heat transfer and thermal systems
Crossflow effectiveness with the larger capacity stream mixed
Single-pass crossflow exchanger with the Cmax fluid mixed transversely and the Cmin fluid unmixed.
- Ref
- HTS-42
- Rev
- v1
- Field
- Heat transfer and thermal systems
- Result
- ε
For a single-pass crossflow exchanger with the larger-capacity (Cmax) stream mixed transversely and the Cmin stream unmixed, ε = {1 − exp[−Cr(1 − exp(−NTU))]}/Cr. When Cr = 0, as in boiling or condensing, it reduces to 1 − exp(−NTU). Specify carefully which stream is mixed, as the other case gives a different result.
Single-pass crossflow exchanger with the Cmax fluid mixed transversely and the Cmin fluid unmixed. At Cr = 0 it reduces to the phase-change limit 1 − e⁻ᴺᵀᵁ.
Calculator
- Phase-change limit (Cr = 0), 1 − exp(−NTU)0.8647
- Reduction against the phase-change limit0.1627
- Parallel-flow effectiveness at the same NTU and Cr0.6335
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The crossflow exchanger transfers 70.2 % of the maximum possible heat, against 86.47 % if the other stream could absorb heat without temperature change.
- A parallel-flow unit of the same size and capacity ratio would reach 63.35 %, so crossflow outperforms it.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| NTU Number of transfer units UA/Cmin | 0 to 20 | 0 | 0.7869 | 0.7869 | +10% | +2.25 % |
| Cr Capacity ratio Cmin/Cmax | 0 to 1 | 0.5788 | 0.8647 | 0.2859 | +10% | −1.98 % |
Sweep of Number of transfer units UA/Cmin
| Number of transfer units UA/Cmin | Effectiveness |
|---|---|
| 0 | 0 |
| 2.5 | 0.7361 |
| 5 | 0.7828 |
| 7.5 | 0.7866 |
| 10 | 0.7869 |
| 12.5 | 0.7869 |
| 15 | 0.7869 |
| 17.5 | 0.7869 |
| 20 | 0.7869 |
Sweep one variable
Variables and how each one contributes
Effectiveness
What the equation gives you. Everything else feeds it.
Number of transfer units UA/Cmin
The number of transfer units, UA/Cmin. Raises the effectiveness, with falling returns. Raising it by 10 % (to 2.2) moves the result by +2.25 %, from 0.702 to 0.7178.
Capacity ratio Cmin/Cmax
The capacity ratio Cmin/Cmax, between 0 and 1. A larger ratio lowers the effectiveness. Raising it by 10 % (to 0.55) moves the result by −1.98 %, from 0.702 to 0.6881.
Worked example with the values above
- Inner term: 1 − exp(−NTU) = 0.86466; × Cr = 0.43233.
- Outer term: 1 − exp(−0.43233) = 0.35101.
- ε = 0.35101 / 0.5 = 0.70201.
Assumptions and limits
- Steady operation with constant properties and overall coefficient, and an insulated exterior.
- The flow arrangement matches the formula exactly, including which fluid is mixed.
Common mistakes
- Using the formula when the Cmin stream is the mixed one.
- Using it when both streams are unmixed.
- Forgetting the Cr = 0 limit for boiling or condensing duty.
Statistics and uncertainty
Effectiveness formulas are exact for their ideal arrangements, but real exchangers have bypass, leakage and non-uniform flow, which lower performance by a few per cent to 10 %. Fouling allowances are largely judgement.
Where it is used
- Rating exchangers from known UA and flow rates.
- Estimating the effect of fouling on duty.
Maths you need
- Capacity rate: C = ṁcp, in W/K
- NTU: UA divided by Cmin
- Effectiveness: actual heat transfer over the thermodynamic maximum